Dynamic Calibration of Force Platforms by Means of

a Parallel Robot

E. Brau

, J. Cazalilla

, M. Vallés

, A. Besa

, A.Valera

, V. Mata

and A. Page

1,4

Instituto de Biomecánica de Valencia, Universitat Politècnica de Valencia, València, Spain

Departamento de Ingeniería de Sistemas y Automática, Universitat Politècnica de València, València, Spain

Departamento de Ingeniería Mecánica y de Materiales, Universitat Politècnica de València, València, Spain

Grupo de Tecnología Sanitaria del IBV, CIBER de Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN V.),

València, Spain

Keywords: Biomechanics, Force Platform, Calibration, Parallel Robot.

Abstract: Force platforms are the basic equipment to measure ground reaction forces and moments in biomechanical

studies. So, accurate in situ calibration of force platforms is critical for ensuring the accuracy and precision

of the results of experimental studies. Although there are different avaliable approaches for in situ

calibration, most of the existing methods do not use realistic and repeteable force patterns to calibrate

platforms. In this paper, a new technique based on the use of a 3PRS parallel robot for applying a predefined

dynamical load is proposed, where force patterns can be reproduced in a similar way as the used during

actual experimental measures. This robot can be programmed to apply force patterns simulating the

conditions of human gait, running or jumping. Calibration is performed by comparing the forces measured

by the platform and the ones measured by a calibrated load cell. A new algorithm was developed for

correcting the sensitivity coefficients, including an estimation of errors in the orientation of the load cell.

This method has been validated by means of an specific experiment.

1 INTRODUCTION

Force platforms (FP) are the basic device for

measuring forces and moments in biomechanical

studies. Along with human movement analysis

systems, they provide the information necessary for

the development of inverse dynamic models. Hence,

its accuracy is critical in the estimation of the

variables associated with these models (Hatze,

2002).

A standard FP is composed of a flat top plate

supported by four force transducers, usually

piezoelectric or based on strain gauges. Each sensor

provides voltage signals that are transformed into

forces through the sensitivity coefficients obtained

by calibration. Once these forces are measured, it is

possible to compute the resultant force and torque

associated to the ground reaction.

Usually, the sensitivity coefficients of the

transducers are obtained in a calibration process

before they are mounted on the FP. However,

transducers can undergo small changes in their

response over time. There also exist other errors

associated with the cross-talk effects, the orientation

of the transducers or some effects associated to

underload deformations. Therefore, it is necessary to

recalibrate the platform after assembling, and also

periodically, to ensure that measurements are

reliable over time (Schmiedmayer and Kastner,

1999); (Chockalingama et al., 2002).

Several approaches to the recalibration of FP

have been published. The first attempts were static,

based on devices that apply known forces by means

of weights (Hall et al., 1996). Although this kind of

methods is quite simple, the applied forces are static

and they do not reproduce the dynamic effects of

forces during the mesument of actual loads.

Different devices have been proposed to apply

dynamic loads for calibrating FP. Rabuffeti et al.

(2003) used a bar to manually apply a calibration

load, whereas the direction and location of such

force was measured by photogrammetry. The device

proposed by Collins et al. (2009) is similar, but uses

an instrumented bar to fully characterize the applied

load. Another alternative is proposed by Cedraro et

al. (2009) in which a load cell is used to measure the

applied forces. Although all these systems allow

applying dynamic forces, such loads are manually

132

Brau E., Cazalilla J., Vallés M., Besa A., Valera A., Mata V. and Page A..

Dynamic Calibration of Force Platforms by Means of a Parallel Robot.

DOI: 10.5220/0004235901320136

In Proceedings of the International Conference on Biomedical Electronics and Devices (BIODEVICES-2013), pages 132-136

ISBN: 978-989-8565-34-1

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

applied, so they are non-reproducible and rather

deviate from patterns of actual loads during

biomechanical measurements.

Other alternative based on mechanical devices

have been proposed to apply repeatable dynamic

loads. The simplest devices used a pendulum to

generate dynamic loads (Fairburn et al., 2000).

Others use motorized systems that generate forces of

inertia, as proposed by Hsieh et (2011). Although

both systems can reproduce repeteable patterns of

dynamical loads, they are barely versatile and

generate force patterns quite different of those

produced during biomechanical studies, such as

movements during gait, running or jumping.

In addition to the type of device to generate the

reference load, it is necessary to define a calibration

model. The most common used model assumes a

linear relationship between the output signals and

the applied forces and moments (Cappello et al,

2004). Recently, other non-linear models for the

calibration of the COP have been defined (Cappello

et al., 2011; Hsieh et al., 2011). The difference

between using linear or non-linear models is

especially relevant when the loads applied in the

calibration are quite different from those actually

applied during the experiments.

The use of robots can be useful to solve these

problems since they allow a precise and repeatable

generation of dynamical load patterns. In particular,

parallel robots have some interesting characteristics

in terms of accuracy, load capacity and velocity

range, which make them particularly suitable to

simulate dynamic patterns as those which appear in

biomechanical studies (Diaz-Rodriguez et al., 2010).

This paper proposes a method for FP

recalibration by means of a parallel robot

instrumented with a calibrated load cell. This

experimental device allows simulating patterns of

forces similar to the ones produced during walking,

running or any other gesture used in biomechanical

studies. On the other hand, we used a nonlinear

calibration model, which includes an algorithm for

correction of the alignment of the platform and the

reference cell. This algorithm has been validated

through a simulation, while the experimental device

has been applied to the calibration of a trading

platform.

2 MATERIAL AND METHODS

2.1 Calibration Device. Parallel Robot

The calibration tests were performed on a FP

Dinascan-IBV (Farhat et al., 2010). A 3PRS parallel

robot with three degrees of freedom was used to

apply the patterns of forces on the platform (Diaz-

Rodriguez et al., 2010). This robot can be

programmed to implement any predefined load

pattern whitin a wide range of forces and

frequencies (Vallés et al., 2011).

Figure 1: Calibration device. 3PRS parallel robot and

calibrated load cell.

The forces were applied on the platform through a

calibrated load cell (model Delta, ATI - Industrial

Automation), as shown in Figure 1. This cell was

placed in seven positions on the platform, defined by

a calibration grid. A steel ball was located on the cell

to ensure contact at a point. Moreover, a block of

teflon was placed in the contact area of the robot

actuator to prevent friction-induced oscillations.

Two types of load patterns were applied in this

study: a) actual gait patterns, used for the validation

of calibration algorithms, and b) calibration load

patterns consisting of a sinusoidal load of null

minimum value, peak to peak of 500 N and a

frequency of 0,5 Hz.

2.2 Platform Model

The modeled FP was a platform DINASCAN-IBV

(Farhat et al., 2010). This platform uses four sensors

instrumented with strain gauges. Each transducer

uses two channels to measure the vertical force and a

horizontal force component, respectivley. The

equation that relates the applied force and the output

sensor for the transducer k is:

























































dVmVcV

cHdH

SSS

(1)

where V

and V

are the voltage signals measured

by the vertical and horizontal channels, respectively.

and S

are the direct sensitivity coefficients,

whereas S

and S

are the cross-talk sensitivity

coefficients. These coefficients are assumed to be

DynamicCalibrationofForcePlatformsbyMeansofaParallelRobot

133

constant, which seems to give a linear relationship

between applied forces and voltage output.

However, S

is a nonlinear cross-sensitivity

coefficient, that models a nonlinear cross-talk effect

associated to deformation of transducer when a

horizontal force is applied. This deformation affects

in the same way regardless of the direction of the

horizontal force f

; so, S

should change its sign

when f

changes its direction.

Eq. (1) allows to calculate the forces on each

sensor from measured V

and V

. Resultant force

and moment can be calculated as:





HkHkVkVk

ff uuF

(2)

)(





HkHkVkVkkO

ff uurM

(3)

where u

y u

are the unit vectors corresponding to

the vertical direction (OZ axis) and the horizontal

direction associated to sensor k (OX or OY axis,

depending on the transducer). Vector r

is the vector

that defines the location of the centre of transducer k

with respect to centre of the FP, O.

2.3 Recalibration Algorithm

We assume that the measurements obtained with

calibrated load cell are a gold standard. During the

recalibration the load cell was placed at m different

positions (m=7, in our study), and n load forces have

been applied at each position.

denotes the force

measured by the load cell corresponding to the i-th

force (i=1, 2, n) applied at the j-th location (j=1, 2,

..m).

corresponds to the same force, but measured

by the FP. The difference between both values is due

to two main sources of error. On the one hand, there

are some errors associated with errors in the

sensitivity coefficients and also it could be a small

error in the alignment of load cell and FP local

reference systems.

The error associated with the sensitivity

coefficients can be quantified by differentiating (1).

Therefore the error in the force measured by sensor

k-th is:



HvH

fff













































000

(4)

where



is coefficient that represents the sign of f

Having in mind Eq. (2), the difference between

force measured by the load cell and the FP is:



HvH

kVkHk

faff



































000

Suu

FFF

(5)

Equation (5) represents a linear system with 3

equations and 5•k=20 unknowns (k = 4 sensors),

corresponding to the values of dS

=[dS

, dS

] of each sensor. By applying (5) to

the n measurements at the m locations of the load

cell, we obtain a system with 3nm and 20

unknowns that can be solved by least squares. The

computed values of dS

are used to correct the

sensitivity coefficients in an iterative process.

In addition to the error associated with the

sensitivity coefficients, it is necessary to consider

the error of alignement between the FP and the load

cell reference systems. This misalignement can be

described as a small rotation,

d that propagates as

an error in the forces measured by the load cell:

dd FθF 

(6)

Note that the error associated to the misalignment

d is the same for each location of the load cell,

whereas the error in (5) is due to the sensitivity

coefficients, and corresponds to the same

coefficients for any measurement (i, j). Therefore,

can be estimated as the difference between the

measures by the cell and the FP, once the sensitivity

coefficients are corrected. The calculation of

dis

immediate since it is formally identical to the

infinitesimal displacements problem, whose solution

is (Page et al., 2009):









d FFFTθ 





[

(7)

where,

[T] is a matrix similar to the tensor of inertia

of a point cluster, where the point coordinates are

replaced by the components of the forces

Ci.

The recalibration process consists of an iterative

process in which the Eqs. (5) and (7) are

consecutively solved until it converges into a

stationary solution of the sensitivity coefficients.

Two iterations are ussually enough to get a good

solution.

2.4 Validation

Two checks have been performed to validate the

calibration procedure. First, the recalibration

algorithm was validated by means of a simulation

that used data from actual measurements of the

BIODEVICES2013-InternationalConferenceonBiomedicalElectronicsandDevices

134

platform. These data were obtained from real gait

and running movements. The “actual” forces were

calculated from the nominal values of the sensitivity

coefficients and the voltage signals measured by the

transducers.Then, a random error of 10% was added

to the sensitivity coefficients, thus obtaining the

forces corresponding to the "uncalibrated" FP.

Using these data, the proposed recalibration

algorithm has been applied, and the results were

compared with those obtained with a recalibration

matrix as it is proposed in the literature (Collins et

al, 2009).

The second validation consisted of an

experiment. The platform was recalibrated by

applying a senoidal forces with a null minimum

value, peak to peak value of 500 N and a frequency

of 0.5 Hz. The load cell was placed at seven

different positions and loads with different

orientations of the horizontal force applied at each

location.

3 RESULTS

Figure 2 shows the results of a simulation with a gait

force pattern (left side) and a running pattern (right

side). The blue dotted line corresponds to the

"actual" forces calculated from the nominal

sensitivity coefficients and the voltage output of the

transducers. Red line represents the forces

corresponding to the “uncalibrated FP”, calculated

after introducing an error in the sensitivity

coefficients. These errors are large, especially in the

vertical force. Finally, the solid blue line represents

the force obtained after correcting the errors in the

sensitivity coefficients from the proposed algorithm.

Only two iterations were used.

Figure 2: Force patterns in the validation of the calibration

algorithm by simulation.

Table 1 shows the rms values of the errors,

expressed as a percentage of the actual value. The

first column shows the errors in each component of

the force. The second one displays the errors that

would be obtained if a matrix of recalibration had

applied, assuming a linear model. As it can be seen,

the linear approximation provides good

recalibration; however, important errors remain in

the Y component, probably due to the non-linear

nature of the S

coefficient. The X and Z

components present smaller errors. When the

proposed model of FP is applied, the residual errors

are very small, less than 1% in all cases.

Table 1: RMS of errors in force components (% of the

actual values).

Uncalibrated

After linear

recalibration

After recalibration with

the proposed model

4.6% 1.8% 0.1%

Y

14.1% 1.1% 0.5%

20.0% 7.6% 0.4%

Table 2 shows the results of the experimental

validation. In this case, the nominal sensitivity

coefficients of the platform were used as initial data.

For these values, the initial error is not too large in

absolute values, which indicates that the coefficients

used in the previous calibration have not

experienced large variations. The greater relative

errors of horizontal components are due to the small

amplitude of such forces in the experiment (around

60 N). However, after applying the recalibration

procedure we obtain an improvement of 30% in the

case of the horizontal forces. On the contrary, the

improvement in the error in the vertical component

is not noticeable. In any case, the results show that

the proposed method allows to effectively

recalibrating FP by using dynamic force patterns.

Table 2: RMS values of force errors before and after the

recalibration process (Newton; in parentheses as a

percentage of the peak to peak values).

Before recalibration After recalibration

X component

4.8 N (8.1%) 2.9 N (4.9%)

Y component

5.3 N (8.8%) 3.9 N (6.5%)

Z component

7.7 N (1.5%) 6.7 N (1.3%)

4 DISCUSSION AND

CONCLUSIONS

This paper presents a device for calibrating FP based

on a 3PRS parallel robot. The robot was

programmed to apply forces similar to those

DynamicCalibrationofForcePlatformsbyMeansofaParallelRobot

135

produced in human gait and running.

Parallel robots can generate dynamic forces in a

realistic and repeatable way. In this sense, realism is

improved compared to static calibration systems

(Hall et al., 1996) or dynamic systems using

mechanical devices, which do not represent real

efforts during clinical applications (Fairburn et al.,

2000); (Hsieh et al., 2011)

Moreover, the system allows programming any

kind of force in a wide range of amplitudes and

temporal patterns, which improves other manual

systems as described by other authors (Rabuffeti et

al., 2003); (Collins et al., 2009); (Cedraro et al.,

2009). The robot is able to apply cyclic repeatable

forces, allowing analyzing effects such as hysteresis

or potential drifts of the sensors.

We also propose a recalibration algorithm that

allows characterizing the sensitivity coefficients of

each sensor. The procedure is not based on a linear

recalibration matrix, but performs the calibration of

each sensor using a nonlinear model. This model

also includes a process for correcting the orientation

of the load cell used as a reference. The results

obtained show that this procedure offers better

results than some systems based on linear models.

In short, parallel robots are robust and versatile

devices able to generate dynamic load patterns

similar to the forces that appear in biomechanical

studies. Combined with a suitable calibration

algorithm, they can be very useful for dynamic

calibration of FP.

ACKNOWLEDGEMENTS

This work has been funded by the Spanish

Government and co-financed by EU FEDER funds

(Grants DPI2009-13830-C02-01, DPI2009-13830-

C02-02 and IMPIVA IMDEEA/2011/ 93).

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